lecture10 ee720 jitter
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Sam Palermo Analog & Mixed-Signal Center
Texas A&M University
ECEN720: High-Speed Links Circuits and Systems
Spring 2013
Lecture 10: Jitter
Agenda
• Jitter Definitions
• Jitter Categories
• Dual Dirac Jitter Model
• System Jitter Budgeting
• Reference Material • Jitter application notes posted on website • Majority of today’s material from Hall reference
2
Eye Diagram and Spec Mask
• Links must have margin in both the voltage AND timing domain for proper operation
• For independent design (interoperability) of TX and RX, a spec eye mask is used
3
Eye at RX sampler
RX clock timing noise or jitter (random noise only here)
[Hall]
Jitter Definitions
• Jitter can be defined as “the short-term variation of a signal with respect to its ideal position in time”
• Jitter measurements • Period Jitter (JPER)
• Time difference between measured period and ideal period
• Cycle to Cycle Jitter (JCC) • Time difference between two adjacent clock periods • Important for budgeting on-chip digital circuits cycle time
• Accumulated Jitter (JAC) • Time difference between measured clock and ideal trigger clock • Jitter measurement most relative to high-speed link systems
4
Jitter Statistical Parameters
• Mean Value • Can be interpreted as a fixed timing offset or “skew” • Generally not important, as usually can corrected for
• RMS Jitter • Useful for characterizing random component of jitter
• Peak-to-Peak Jitter • Function of both deterministic (bounded) and random
(unbounded) jitter components • Must be quoted at a given BER to account for random
(unbounded) jitter
5
Jitter Calculation Examples
6
n 1 2 3 4 Mean RMS PP
JPER -0.06 0.02 -0.06 0.12 0.005 0.085 0.18
JCC 0.08 -0.08 0.18 - 0.06 0.131 0.26
JAC -0.07 -0.05 -0.11 0.01 -0.055 0.05 0.12
JPER = time difference between measured period and ideal period JCC = time difference between two adjacent clock periods JAC = time difference between measured clock and ideal trigger clock
Jitter Histogram
• Used to extract the jitter PDF • Consists of both deterministic and random components
• Need to decompose these components to accurately estimate jitter at a given BER
7
[Hall]
0 UI t
High and Low Signal Voltage Distribution at Time t
Threshold (Zero) Crossing Time Distribution
Jitter Categories
8
Random Jitter (RJ)
• Unbounded and modeled with a gaussian distribution • Assumed to have zero mean value • Characterized by the rms value, σRJ
• Peak-to-peak value must be quoted at a given BER
• Originates from device noise • Thermal, shot, flicker noise
9
( ) 2
2
2
21
RJ
t
RJ
etRJ σ
σπ
−
=
Deterministic Jitter (DJ) • Bounded with a peak-to-peak value that can be predicted • Caused by transmission-line losses, duty-cycle distortion, spread-
spectrum clocking, crosstalk • Categories
• Sinusoidal Jitter (SJ or PJ) • Data Dependent Jitter (DDJ)
• Intersymbol Interference (ISI) • Duty Cycle Distortion (DCD) • Bounded Uncoirrelated Jitter (BUJ)
10
Sinusoidal or Periodic Jitter (SJ or PJ)
• Repeats at a fixed frequency due to modulating effects • Spread spectrum clocking • PLL reference clock feedthrough
• Can be decomposed into a Fourier series of sinusoids
11
( ) ( )∑ +=i
iii tAtSJ θωcos
• The jitter produced by an individual sinusoid is
( )
≤
>−=
tA
tAtAtPDFSJ
0
122π
Data Dependent Jitter (DDJ)
• Data dependent jitter is correlated with either the transmitted data pattern or aggressor (crosstalk) data patterns
• Caused by phenomena such as phase errors in serialization clocks, channel filtering, and crosstalk
• Categories • Duty Cycle Distortion (DCD) • Intersymbol Interference (ISI) • Bounded Uncorrelated Jitter (BUJ)
12
Duty Cycle Distortion (DCD)
• Caused by duty cycle errors in TX serialization clocks and rise/fall delay mismatches in post-serialization buffers
• Resultant PDF from a peak-to-peak duty cycle distortion (αDCD) is the sum of two delta functions
13
( )
++
−=
2221 DCDDCD
DCD tttPDF αδαδ
Intersymbol Interference (ISI)
• Caused by channel loss, dispersion, and reflections • Equalization can improve ISI jitter
14
No Equalization
2-tap TX Equalization
Bounded Uncorrelated Jitter (BUJ)
• Not aligned in time with the data stream
• Most common source is crosstalk
• Classified as uncorrelated due to being correlated to the aggressor signals and not the victim signal or data stream
• While uncorrelated, still a bounded source with a quantifiable peak-to-peak value
15
Total Jitter (TJ)
• The total jitter PDF is produced by convolving the random and deterministic jitter PDFs
16
( ) ( ) ( )( ) ( ) ( ) ( ) ( )tPDFtPDFtPDFtPDFtPDF
tPDFtPDFtPDF
BUJISIDCDSJDJ
DJRJJT
****
==
where
Jitter and Bit Error Rate • Jitter consists of both
deterministic and random components
• Total jitter must be quoted at a given BER • At BER=10-12, jitter ~1675ps
and eye width margin ~200ps • System can potentially achieve
BER=10-18 before being jitter limited
17
Dual Dirac Jitter Model
• For system-level jitter budgets, the dual Dirac model approximates the complex total jitter PDF and allows for the budgeting of deterministic and random jitter components
18
( ) 2
2
2
21
RJ
t
RJ
etRJ σ
σπ
−
=
( ) ( ) ( )2
2/2
2/ δδδδ δδ DJtDJttDJ ++
−=
( ) ( ) ( )
+==
+−
−− 22 2
2/2
2/
221* RJRJ
DJtDJt
RJ
eetDJtRJtJT σσδδδδ
σπ
Dual Dirac Jitter Model
• Jitter at a given BER is computed considering both leading and trailing edges
19
( ) ( )
( ) ∫∞
−=
+−+
−−=
++
−=
t
x
RJRJtrail
RJRJlead
dxeterfc
DJtUIerfcDJtUIerfctBERDJterfcDJterfctBER
22
22/
22/5.0
22/
22/5.0
π
σσσσδδδδδδδδ
where
,
Dominant Terms t
Dual Dirac Jitter Model Example
20
• Plot measured jitter PDF vs Q-scale
( )
0.5 typically density, transition the is where Tρρ
−= −
TBER
BERerfBERQ 12 1
• Tails are used to extract σRJ
• Extrapolate to Q(0) to extract separation of dual-Dirac delta functions peak value-to-peakjitter ticdeterminis Actual
functions delta Dirac-dual of seperation Extracted
=
=
ppDJ
DJδδ
Dual Dirac Jitter Model Example
21
• Extracted dual Dirac model matches well with measured jitter PDF
+==
+−
−− 22 2
2/2
2/
221PDF Dirac-Dual RJRJ
DJtDJt
RJ
ee σσδδδδ
σπ
System Jitter Budget
• For a system to achieve a minimum BER performance
22
( ) ( )sysQsysDJUI RMSBERσδδ +≥
• The convolution of the individual deterministic jitter components is approximated by linear addition of the terms
( ) ( )∑=i
iDJsysDJ δδδδ
• The convolution of the individual random jitter components results in a root-sum-of-squares system rms value
( ) ( )∑=i
RMSRMS isys 2σσ
Jitter Budget Example – PCI Express System
23
Architecture
Jitter Model
[Hall]
Jitter Budget Example – PCI Express System
24
( ) ( ) ( ) ( ) ( )clockDJRXDJchannelDJTXDJsysDJ δδδδδδδδδδ +++=
( ) ( ) ( ) ( ) ( )clockRXchannelTXsys RMSRMSRMSRMSRMS2222 σσσσσ +++=
6.15 * 14.069 =
[Hall]
160
Next Time
• Clocking Architectures
25
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